Every human being may have their own deffinition of " happiness "and "freedom " . And to someone freedom means happiness or happiness means different sort of freedom . So I think sometimes happiness may exist with freedom together , and when they are seperated you will neither feel happiness or freedom .
And when the question comes to me , i may give up happiness when i want to spend the whole week to study English . but definitely i will also feel happiness inerside,and i will also feel more freedom with this language. There is a great ancient philosopher 庄子 ， He thought the question all his life ,and he thought his freedom is his happiness. :)